Categories for the Working Mathematician: 5 (Graduate Texts in Mathematics, 5) ISBN-978-0387984032

A range of general concepts that are helpful in many different domains are provided by Categories for the Working Mathematician. This book explains the ideas of category, functor, natural transformation, and duality, beginning with the fundamentals. After that, the book discusses adjoint functors, which offer a way to work with direct and inverse limits, an analysis of functor representations by sets of morphisms, and a description of universal constructions. The subsequent chapters provide several examples of these category ideas, including numerous uses of the fundamental existence theorem for adjoint functors. Beck’s theorem characterizes the categories of algebraic systems, which are built from specific adjoint-like data. Following a review of several applications, the book moves on to the development and utilization of Kan extensions.